At present neutral atomic hydrogen (HI) gas in galaxies at redshifts above $z sim 0.3$ (the extent of 21-cm emission surveys in individual galaxies) and below $z sim 1.7$ (where the Lyman-$alpha$ line is not observable with ground-based telescopes) has remained largely unexplored. The advent of precursor telescopes to the Square Kilometre Array will allow us to conduct the first systematic radio-selected 21-cm absorption surveys for HI over these redshifts. While HI absorption is a tracer of the reservoir of cold neutral gas in galaxies available for star formation, it can also be used to reveal the extreme kinematics associated with jet-driven neutral outflows in radio-loud active galactic nuclei. Using the six-antenna Boolardy Engineering Test Array of the Australian Square Kilometre Array Pathfinder, we have demonstrated that in a single frequency tuning we can detect HI absorption over a broad range of redshifts between $z = 0.4$ and $1.0$. As part of our early science and commissioning program, we are now carrying out a search for absorption towards a sample of the brightest GPS and CSS sources in the southern sky. These intrinsically compact sources present us with an opportunity to study the circumunuclear region of recently re-started radio galaxies, in some cases showing direct evidence of mechanical feedback through jet-driven outflows. With the sensitivity of the full ASKAP array we will be able to study the kinematics of atomic gas in a few thousand radio galaxies, testing models of radio jet feedback well beyond the nearby Universe